Subgroups — #19098903

Order 5056.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14579137	C₂	1	1	yes	maximal, characteristic
2	#14579119	C₂	1	1	yes	maximal, characteristic
3	#14579095	C₂	1	1	yes	maximal, characteristic, complemented
4	#14579092	C₂	1	1	yes	maximal, characteristic, complemented
5	#14579085	C₂	1	1	yes	maximal, characteristic, complemented
6	(C₂×D₇₉)⋊C₈	C₂	1	1	yes	maximal, characteristic
7	#103×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₇₉	C₂²	1	1	yes	characteristic
9	C₂×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
12	Dic₇₉⋊C₄	—	2	1	no	—
13	(C₂×D₇₉)⋊C₄	—	2	1	no	—
14	(C₂×D₇₉)⋊C₄	—	2	1	no	—
15	C₄×Dic₇₉	—	2	1	no	—
16	C₂×Q₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₇₉	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
19	C₂²×D₇₉	D₄	1	1	yes	characteristic
20	Q₈×C₇₉	—	2	1	no	—
21	Q₈×C₇₉	—	2	1	no	—
22	C₂×C₄×C₇₉	—	2	1	no	—
23	C₂×C₄×C₇₉	—	2	1	no	—
24	C₂×C₄×C₇₉	C₂³	1	1	yes	characteristic
25	C₂×Dic₇₉	—	2	1	no	—
26	C₂×Dic₇₉	—	2	1	no	—
27	C₂×Dic₇₉	D₄	1	1	yes	characteristic
28	C₄×D₇₉	—	2	1	no	—
29	C₄×D₇₉	—	2	1	no	—
30	C₈×C₇₉	—	2	1	no	—
31	C₇₉⋊C₈	—	2	1	no	—
32	C₂²×C₇₉	C₂×D₄	1	1	yes	characteristic
33	C₂×D₇₉	—	2	1	no	—
34	C₂×D₇₉	—	2	1	no	—
35	C₂×D₇₉	—	2	1	no	—
36	C₄×C₇₉	—	4	1	no	—
37	C₄×C₇₉	—	4	1	no	—
38	C₄×C₇₉	#41	1	1	yes	characteristic
39	C₄×C₇₉	#41	1	1	yes	characteristic
40	Dic₇₉	—	2	1	no	—
41	Dic₇₉	—	4	1	no	—
42	Dic₇₉	—	4	1	no	—
43	C₂×C₇₉	#123	1	1	yes	characteristic
44	C₂×C₇₉	#135	1	1	yes	characteristic
45	C₂×C₇₉	#137	1	1	yes	characteristic
46	D₇₉	—	4	1	no	—
47	C₇₉	#485	1	1	yes	characteristic, complemented, Sylow
48	#485	—	79	1	no	maximal, Sylow
49	C₂²⋊Q₈	—	79	1	no	—
50	#117	—	79	1	no	—
51	#107	—	79	1	no	—
52	#106	—	79	1	no	—
53	#103	—	79	1	no	—
54	#103	D₇₉	1	1	yes	characteristic, complemented
55	C₂²⋊C₈	—	79	1	no	—
56	C₂×Q₈	C₂×D₇₉	1	1	yes	characteristic
57	C₂²×C₄	—	79	1	no	—
58	C₂×C₈	—	79	1	no	—
59	C₂×C₈	C₂×D₇₉	1	1	yes	characteristic
60	C₄⋊C₄	—	79	1	no	—
61	C₄⋊C₄	—	79	1	no	—
62	C₄⋊C₄	—	158	1	no	—
63	C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
64	C₂²⋊C₄	—	158	1	no	—
65	C₂²⋊C₄	—	158	1	no	—
66	C₄²	—	158	1	no	—
67	C₂³	—	79	1	no	—
68	Q₈	—	2	1	no	—
69	Q₈	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	79	1	no	—
73	C₂×C₄	—	158	1	no	—
74	C₂×C₄	—	158	1	no	—
75	C₂×C₄	—	158	1	no	—
76	C₂×C₄	—	158	1	no	—
77	C₂×C₄	C₂²×D₇₉	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	158	1	no	—
80	C₂²	—	158	1	no	—
81	C₂²	—	158	1	no	—
82	C₂²	—	158	1	no	—
83	C₂²	D₄×D₇₉	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	316	1	no	—
87	C₄	—	316	1	no	—
88	C₄	—	158	1	no	—
89	C₄	#11929623	1	1	yes	characteristic
90	C₄	#11929624	1	1	yes	characteristic
91	C₂	—	316	1	no	—
92	C₂	#14579143	1	1	yes	characteristic
93	C₂	#14579184	1	1	yes	characteristic
94	C₂	#14579190	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³
Frattini	C₂×C₄	C₂²×D₇₉
Fitting	#103×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₄
hypercenter	#103	D₇₉
hypocenter	C₇₉	#485
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. #14579095	C₂	semidirect
4. #14579092	C₂	semidirect
5. #14579085	C₂	semidirect
7. #103×C₇₉	C₂	semidirect
47. C₇₉	#485	semidirect
54. #103	D₇₉	semidirect